This is the basic construction that we want to carry out in more complicated situations. By that we mean that the fields in the correlation function will be allowed to carry arbitrary spins (in general, different from each other). In such a case the above procedure meets some difficulties. Firstly, although conformal blocks are still characterised as solutions to appropriate Casimir equations, it is often hard to identify them in the world of special functions. For bosonic theories, there exist efficient algorithmic procedures for computation of such spinning blocks, [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}. One systematic and efficient method is to start from scalar blocks and apply to them a set of differential operators known as weight-shifting operators (see also [10]}, [11]}, [12]} for other investigations of bosonic conformal blocks). It is probably fair to say that the theory of superconformal blocks is considerably less developed than its bosonic counterpart.
